DAT missed questions
Currently, Tommy is five times as old as Bianca. In eight years, Tommy will only be three times as old as Bianca. How old is Tommy right now? A. 8 B. 16 C. 24 D. 32 E. 40
Answer: E. 40 This is a question involving the ratio of ages. To solve this question, we should first start by writing an equation with the information given. Let the ages of Tommy and Bianca in the present be T and B respectively. STEP 1: Let: T = 5B T + 8 = 3 (B+8) STEP 2: We can substitute T with 5B since the two variables are equal, to create: 5B + 8 = 3 (B + 8) STEP 3: Finally, we can expand and solve: 5B + 8 = 3B + 24 2B = 16 B = 8 T = 5B = 5 x 8 = 40 Therefore, Tommy is currently 40-years old
The probability that Joe wins his first boxing match is 0.47. The probability that Joe wins his second boxing match is 0.85. What is the probability that Joe wins at least one of these two matches? A. 0.50 B. 0.61 C. 0.75 D. 0.85 E. 0.92
E. 0.92 STEP 1: The probability that Joe loses his first boxing match is 0.53. The probability that he loses his second match is 0.15. The probability that he loses both is the probabilities multiplied together: 0.53 x 0.15 = 0.0795 STEP 2: We can subtract this number from 1 to find the probability that he wins AT LEAST one of the two matches: 1 - 0.0795 = 0.925 The probability that Joe wins at least one match is around 0.92 and therefore, the answer is E.
According to the following reaction, how many grams of Fe2O3 are formed when 383g of iron is combusted? 4Fe + 3O2 → 2Fe2O3
(160)(383)(2)/(56/4) STEP 1: The first step to solving this question is calculating the number of moles of iron (Fe) combusted. We know that the molar mass of iron is 56 g/mol, and from the question, we know that the mass of iron in the reaction is 383g, therefore: mol of fe = mass/molar mass 383/56 STEP 2: From the balanced reaction, we know that every 4 moles of Fe results in the formation of 2 moles of Fe2O3. Therefore, we can solve to determine the moles of Fe2O3: STEP 3: Before we can solve for the mass of Fe2O3, we must first solve for its molar mass as follows: STEP 4: We now know both the moles and molar mass of Fe2O3. The final step is to solve for the mass of Fe2O3 by rearranging the following formula:
A 200g sample of mercury at 25°C was heated to 75°C with the addition of 3kJ of energy. Calculate the specific heat of mercury in J/g°C.
(3000)/(200)(50) STEP 1: To determine the answer to this question, we need to utilize the following equation: q = mcΔT q = heat gained (positive value) or lost (negative value)c = specific heat capacity of an object at a given state (changes depending on whether it's liquid, solid or vapor phase)ΔT = final temperature - initial temperature Note: When using this equation, it is important to make sure that the units are identical in order for them to cancel out. Also, be sure to convert 3KJ to 3000 Joules OR change the units for specific heat to KJ/g°C. STEP 2: To solve, simply plug in the values into the equation in order to derive the answer: q = mcΔT → c = q/mΔT c = (3000J) / (200g * (75°C - 25°C)) c = (3000) / (200*50)
Out of a 50 member class, 36 play basketball, 18 play baseball, and 8 play both. How many members of the class do not play either sport? A. 4 B. 8 C. 10 D. 14 E. 18
A. 4 STEP 1: To find the number of people who play basketball only, we can subtract the amount of people who play basketball from those who play both: 36 - 8 = 28 people who only play basketball. STEP 2: To find the number of people who play baseball, we simply repeat the above process: 18 - 8 = 10 people who only play baseball. STEP 3: Since the number of people who play both is a value that has already been given to us (8 people play both baseball and basketball), we can move on to find the number of people who play at least one sport: 28 (basketball) + 10 (baseball) + 8 (both) = 46 people play at least one sport. We can also arrive at the same answer by adding the total amount of people who play basketball and the total amount of people who play baseball and subtract the overlap (which would've been counted twice): 36 + 18 - 8 =46 people play at least one sport STEP 4: Now, since we know the class has 50 people, the number of people who play neither sport can be represented by the total number of people minus the people who play at least one sport: 50 - 46 =4 people play neither basketball nor baseball
Adaptive radiation is best described as A. The emergence of multiple lineages from a single ancestral species B. Process where a species can produce more offspring C. Radiation that prevents a species from adapting to an environment D. Process in which a species best adapts to its environment E. The emergence of an adapted species over one generation
A. The emergence of multiple lineages from a single ancestral species
A NaOH solution has a molarity of 2.00 M and is titrated with 75.0 mL of 0.500 M H2SO4. What volume of NaOH is needed to reach the end point? A. 0.01875 L B. 0.03750 L C. 0.0500 L D. 0.0750 L E. 0.1500 L
B. 0.03750 L STEP 1: To determine the answer, we start by writing the chemical reaction and balancing it. H2SO4 + 2NaOH → Na2SO4 + 2H2O STEP 2: Now, we can determine the moles of H2SO4. moles of H2SO4 = Molarity x Volume moles of H2SO4 = (0.500 mol/L) (0.0750 L) = 0.0375 mol STEP 3: Next, we determine the number of moles of NaOH required to neutralize all of the H2SO4. Remember, two moles of NaOH is required to neutralize one mole of H2SO4. moles of NaOH = (0.0375 mol) (2) = 0.0750 mol STEP 4: Lastly, we can calculate the volume of NaOH required. (0.0750 mol) / (2.00 mol/L) = 0.03750 L Pro-Tip: One way to solve this calculation easier is by keeping in mind that anything multiplied by 0.5 is like dividing by 2. Therefore, (0.0750L)(0.500 mol/L) is the same as (0.0750L)/(2).
Hose A takes 0.75 hours to fill the swimming pool. Hose B takes 1.5 hours to fill the same pool. How many minutes does it take to fill the swimming pool if both hoses are operating at the same time? A. 15 minutes B. 30 minutes C. 45 minutes D. 75 minutes E. 150 minutes
B. 30 minutes STEP 1A: Since the final answer is in minutes, it will be easier to convert all the units to minutes first. For every minute that it's running, Hose A can fill up 1/45 of the pool. Hose B can fill up 1/90 of the pool during the same amount of time. Therefore, the two hoses acting together can fill up the pool in one minute according to the following expression: 1/45 + 1/90 = 1/x When we solve that equation, we get 3/90 or 1/30. If the two hoses together fill up 1/30 of the pool in 1 minute, it will take 30 minutes to fill up the entire pool if both hoses are working in tandem. STEP 2A: Alternatively, a student could use rates to solve the problem. To avoid working with decimals, we'll first convert 0.75 hours to 45 minutes and 1.5 hours to 90 minutes. Hose A can fill up the pool at a rate of: 1 pool/45 min and Hose B can fill up the pool at a rate of: 1 pool/90 minutes STEP 2B: Therefore, the two hoses acting together can fill up the pool at a rate of: 1 pool/45 min + 1 pool/90 minutes = 1 pool/x minutes STEP 2C: After adjusting for a common denominator, we get: 2 pool/90 min + 1 pool/90 minutes = 3 pool/90 minutes STEP 2D: Now that we know the combined rate, we can set up a simple proportion and cross-multiply to solve for the time it takes to fill 1 pool: 1 pool/x minutes = 3 pool/90 minutes 3x = 90 x = 30 min Therefore, the answer is B.
A sock drawer contains 7 pairs of red socks, 4 pairs of blue socks and 2 pairs of yellow socks. What is the probability that two socks selected at random, without replacement, are both red? A. 1/4 B. 7/25 C. 49/169 D. 7/26 E. 5/12
B. 7/25 To solve this problem, we must first correctly identify it as a probability problem without replacement. Also, note that the amount of socks is given in pairs, but the socks that are drawn are individual. STEP 1: Firstly, we should figure out the total number of socks: 26 socks total STEP 2: The probability of drawing both red socks is the probability of first drawing a red sock multiplied by the probability of drawing a second red sock, accounting for the lack of replacement. 14 red socks/26 socks X 13 remaining red socks/25 remaining socks 7/13 x 13/25 = 7/25
In order to recreate primitive earth's atmosphere, which of the following sets of gases would be required? A. N2, H2O, CO2, NO2 B. CH4, H2, H2O, NH3 C. NO, H2, H2O, CO2 D. NH3, H2, CO3, O2 E. CO, H2, H2O, NO2
B. CH4, H2, H2O, NH3 Therefore, based on the Miller-Urey experiment, it was determined that the following gases were present in the primitive atmosphere: NH3, H2O, H2, and CH4, as shown in the image below.
Which one of the following properties applies to alkaline earth metals? A. Dull B. Form 2+ cations C. High density D. Low boiling point E. Low melting point
B. Form 2+ cations The Alkaline Earth Metals are six elements in group 2 of the periodic table. They are beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra), as show in the image below. These elements have the following properties: • Appear shiny, silvery-white • Are somewhat reactive metals • Have high melting and boiling points • Form 2+ cations since they have a valance of 2 electrons in their outer shell
Osteoporosis is a disease that causes excessive bone resorption in individuals suffering from it. This excessive bone resorption can lead to A. Decreased calcium levels B. Increased phosphorus levels C. Increased parathyroid hormone levels D. Decreased calcitonin levels
B. Increased phosphorus levels One crucial role of the skeletal system is to store minerals that are required by the body to properly function. Two prominent minerals that make up the bone matrix are calcium and phosphorus; these minerals can be released back into the bloodstream when bone resorption occurs. Bone resorption is the breakdown of bone by osteoclasts. When blood calcium levels are low, parathyroid hormone (PTH) is released and stimulates osteoclasts to breakdown bone to release calcium and phosphorus. As blood calcium levels return to normal, negative feedback inhibits the release of PTH. When blood calcium or phosphorus levels are high, calcitonin is released to inhibit bone resorption.
If a 4L solution is 80% concentrated lime juice and 20% water, how much 30% concentrated lime juice must be added so that the concentration of the resulting solution is 50% concentrated lime juice? A. 3L B. 4L C. 6L D. 8L E. 10L
C. 6L STEP 1: First, let's see how much lime juice exists in the 4L solution: STEP 2: The question wants to know how much 30% concentrated lime juice we can add to reach a total final concentration of 50%. That means we want to set up an equation to solve as follows: We can rewrite 50% as 1/2. STEP 3: Now, let's try to set up this equation with a variable we can solve for. As we determined in the first step, we already have 3.2L of concentrated lime juice. To add to that, we will also have 30% of the unknown volume (X) of juice we're adding. In other words: STEP 4: How about total volume? We started with 4L, and we're adding the unknown volume (X) of the lime juice solution. Plugging these in, we have: STEP 5: Cross-multiply and solve: Therefore, the answer is 6L.
Which of the following is TRUE for a reaction occurring at 25°C that has a positive ΔH value? A. The reaction will be spontaneous for any value of ΔH B. The reaction will be non-spontaneous for any value of ΔS C. The reaction will be spontaneous if ΔH < ΔS D. The reaction will be spontaneous only if ΔH > ΔS E. The reaction will be non-spontaneous when ΔH>0 and ΔH = ΔS
C. The reaction will be spontaneous if ΔH < ΔS A spontaneous process occurs naturally under certain conditions, in which it releases free energy and moves to a lower, more thermodynamically stable energy state. A non-spontaneous process, on the other hand, will not take place unless it is "driven" by the continual input of energy from an external source. Note: The spontaneity of a process is not correlated to the speed of the process. Some might be really slow but still considered as a spontaneous process. For a reaction to be spontaneous, ΔG (Gibbs free energy) needs to be a negative number. Based on the equation ΔG = ΔH -TΔS, we can see that in order for a reaction to be spontaneous (negative ΔG), then ΔH (enthalpy) needs to be exothermic (negative) and ΔS (entropy/disorder) needs to be increasing. However, a reaction can have a negative ΔG value even with an endothermic reaction (positive ΔH) as long as the -TΔS value is larger (i.e. more negative) than the positive ΔH, and vice-versa for a negative ΔH value. Here is a quick summary of ΔG and what its value means for the DAT: • Negative: the process is spontaneous and may proceed in the forward direction as written. • Positive: the process is non-spontaneous as written, but it may proceed spontaneously in the reverse direction. • Zero: the process is at equilibrium, with no net change taking place over time.
If you pick three letters from the word ANTEATER with replacement, what is the probability that all three letters are vowels? A. 1/2 B. 1/4 C. 1/6 D. 1/8 E. 1/12
D. 1/8 STEP 1: First, we should separate the letters into vowels and consonants: Vowels: AEAE Consonants: NTTR STEP 2: Then, we can represent the probability of picking a vowel as: P (vowel) = 4 vowels/8 letters = 1/2 STEP 3: Since we replace the "missing" letter every time, the probability does not change from the first pick to the second pick and so on. Thus, the probability of picking three vowels in three letters can be represented by: P (3 vowels) Therefore, the answer is D. 1/2 X 1/2 X 1/2 = 1/8
Station X and Station Y are 480 miles apart. A train starts at a certain time from Station X headed towards Station Y at 60 mph. Two hours later, a train departs from Station Y headed towards Station X and 48 mph. How far from Station X do the two trains meet? A. 108 miles B. 180 miles C. 240 miles D. 320 miles E. 400 miles
D. 320 miles This is a distance and speed problem. To set up the problem, let the time travelled by Train X (from Station X) be (t), and the time travelled by Train Y be (t-2), where t is in hours. By the time the trains have met, they must have covered the entire 480 mile distance. STEP 1: We can set-up the equation as follows: 60(t) + 48 (t-2) = 480 STEP 2: Next, we can expand and simplify: 60(t) + 48(t) - 96 = 480 108t = 576 t = 5.33 hr x 60 miles = 320 miles STEP 3: Train X travelled for 5.33 hours before encountering Train Y. Since Train X is travelling at 60 mph, we can use the distance = speed × time formula to calculate the total distance (from Station X).
For the reaction below, which of the following sets of coefficients would balance the reaction? __HNO3 + __S → __H2SO4 + __NO2 + __H2O A. 4, 1, 1, 4, 4 B. 6, 1, 1, 6, 4 C. 4, 1, 1, 4, 2 D. 6, 1, 1, 6, 2 E. 4, 2, 2, 4, 6
D. 6, 1, 1, 6, 2 STEP 1: To solve this question, we must first determine which element to start balancing first. There are four elements involved in balancing this reaction: H, N, O, and S. Out of these four elements, it's best to start balancing oxygen as it's the only element that can be definitely balanced on both sides without possibly encountering any issues in the future. STEP 2: Next we can balance oxygen on both sides. We can see that it is found in one molecule on the left but three different molecules on the right. The only way we can balance both sides evenly is if we can put a coefficient of 6 on HNO3 and balance the right-side. 6 HNO3 + __S → 1 H2SO4 + 6 NO2 + 2 H2O STEP 3: From the previous step, we have balanced most of the reaction. Finally, we can balance sulphur using a coefficient of 1 on S on the left and a coefficient of 1 on H2SO4 on the right. 6 HNO3 + 1 S → 1 H2SO4 + 6 NO2 + 2 H2O
Which of the following elements exists as a diatomic gas in its standard state and contains a double covalent bond? A. Krypton B. Oxygen C. Nitrogen D. Bromine E. Chlorine
D. Bromine
A student wishes to conduct an experiment where he leaves two identical plates of yeast growing in a sugar solution. He seals one of the plates and incubates both plates overnight. Which of the following substances would be found in the sealed plate but not in the open plate? A. Glucose B. Methanol C. Lactic acid D. Ethanol E. Pyruvate
D. Ethanol 1. When we seal the plates, we are effectively depleting the oxygen content. Thus, the yeast in the sealed plate will begin undergoing anaerobic. 2. Anaerobic respiration in yeasts and plants yields different products than aerobic respiration in animal cells. In anaerobic conditions, organisms such as bacteria, plants and fungi (i.e yeasts) undergo "alcohol fermentation" to produce carbon dioxide and ethanol. In contrast, animal cells will produce carbon dioxide and lactic acid. Since the question is specifically asking about yeast cells, the answer is ethanol. Fermentation is an anaerobic (when oxygen is not present) pathway for breaking down glucose, which begins with glycolysis. In fermentation, the pyruvate made in glycolysis does not continue through oxidation and the Krebs cycle, and the electron transport chain does not run. The purpose of the reactions in fermentation is to regenerate the electron carrier NAD+. Fermentation allows glycolysis to keep running by ensuring a steady supply of NAD+. In Alcohol fermentation specifically, NADH donates its electrons to a derivative of pyruvate, producing ethanol.
Which of the following changes to the system would result in an equilibrium shift towards the reactants? MgO (s) + CO2 (g) ↔ MgCO3 (s) ∆H = +118 kJ/mol A. Increasing the temperature of the system B. Adding more MgCO3 (s) to the equilibrium C. Increasing the pressure of the system D. Increasing the volume of the system
D. Increasing the volume of the system
What is the bond angle that exists within a molecule of SO3? A. 90 B. 104.5 C. 107 D. 109.5 E. 120
E. 120 • Linear - In a linear model, atoms are connected in a straight line. The bond angles are set at 180°. For example, CO2. • Trigonal planar - Molecules with the trigonal planar shape are somewhat triangular and in one plane. The bond angles are set at 120°. For example, BF3. • Tetrahedral - This shape is found when there are four bonds all on one central atom, with no extra unshared electron pairs. The bond angles between the electron bonds are 109.5°. For example, CH4. • Bent or V-shaped - Has a non-linear shape with an angle of about 105°. For example, H2O.
Which of the following is true regarding enzymes? A. Do not change the rate at which equilibrium is achieved B. Increase the activation energy C. Affect the overall energy change of the reaction (ΔG) D. Ensure that the final state of the reaction is the same as the initial state E. Do not change the equilibrium point of a reaction
E. Do not change the equilibrium point of a reaction
Which of the following hormones has a function that directly raises metabolism? A. Oxytocin B. Aldosterone C. Thyroid-releasing hormone D. Thyroid-stimulating hormone E. Thyroxine
E. Thyroxine Thyroid-releasing hormone (TRH) is produced and secreted by the hypothalamus, which induces the anterior pituitary gland to secrete thyroid-stimulating hormone (TSH), which induces the production of Thyroxine (T4) and triiodothyronine (T3), which influence metabolism. Thus, although TRH and TSH are involved in metabolism, their actions are indirect. Thyroxine is the main hormone secreted into the bloodstream by the thyroid gland. It is the inactive form and most of it is converted to an active form called triiodothyronine. In addition to controlling metabolism Thyroxine plays a vital role in regulating the heart and digestive functions, muscle control, brain development and maintenance of bones. The image below shows an overview of the thyroid system. It can be seen how TRH induces the anterior pituitary gland to secrete TSH, which induces the production of T4 and T3, which then raises metabolism.